# How to prevent students from using modified calculators to cheat on exams?

Recently my faculty (mathematics and statistics) and I have been dealing with widespread cheating due to calculators that have been modified so as to have more functionality than is permitted.

At my university we have a standardized calculator that is to be used for tests. This brand of calculator has limited functionality however recently these calculators have been modified and sold so that students can cheat on tests. We have managed to get a hold of one of them and it appears that the electronics inside have been modified. We have managed to identify the group of individuals responsible for modifying and selling these calculators however we are not sure what to do about it.

Here are the options we have considered so far:

1. Check each calculator individually before tests to see if it has been modified. This is impractical as they don't look any different on the exterior and are no different in weight. We would need to open them all up and look inside.

2. Provide our own calculators to the students. This approach, although better than the last, has its drawbacks. It would be expensive for the department to purchase enough calculators initially and then they would over time break and be lost, resulting in more cost so we would prefer not to go this route for that reason. Additionally, students could still quite easily take a modified calculator of their own into exams and swap it out for the provided one.

3. Change the official calculator model. We could move to a new model of calculator however I suspect this would only be a temporary fix as the group responsible for modifying and selling the calculators could easily switch to modifying the new model.

4. Stop having calculators all together. We would prefer not to resort to this as we don't think forcing students to do lengthy arithmetic calculations is the best way to test them. We could try to avoid such things however sometimes it is simply necessary to ask such questions, for example, in an introductory stats class we would like to ask students to find the standard deviation of a set of data points. Asking them to do this without a calculator seems unfair however we can't simply avoid asking such questions if we want to test the students properly.

5. Taking action against the group responsible for making the calculators. Fortunately this group has been identified, however they are not students at my university so we cannot take direct action against them for academic disintegrity. We would like to take legal action against them if possible however my faculty and I are unsure if there is precedent for such a thing. As far as I can tell they are not committing any crimes. If there is something we could do in this regard please let me know.

6. Simply ignore the problem. This is obviously not ideal as using these calculators gives students a clear advantage over those without them. Additionally, students using them often don't need to learn how to perform various calculations and can instead just plug in the various values and have the answer come out.

Has anyone has this happen at their institution before? If you have any suggestions as to what we can do in this situation it would be greatly appreciated.

Here is some clarification on the exact nature of the modifications:
To enter into the modified "mode" you type in a sequence of numbers (eg: 1234567) then it enters into the new mode in which you can do many advanced calculations.
pressing the reset button on the back causes it to appear to reset without actually resetting. If you type the password in you will still get back to the modified mode. In this mode formulas can be saved for example.

• Is the modification only allowing more advanced operations to be performed, or does it allow non-calculator features (displaying text, or allowing communication)?
– vsz
Nov 27 '17 at 7:19
• As a former invigilator we used to hand out school-owned calculators at the start of the exam and collect them as students left. We marked them with a highly visible sticker to prevent students from substituting their own devices. Nov 27 '17 at 9:13
• This depends on the course, but for most maths courses it should be possible to tweak the exam problems so that no calculator is needed for the arithmetic. Either have all the π's and logarithms and square roots cancel, or allow answers to contain such expressions. Nov 27 '17 at 9:19
• For the record, any approach where you check/clear the calculators is destined to fail. I wrote programs on my calculator to do most of my math in high school (not to sneak through math classes, I'm just really, really lazy). Teachers started having us clear our RAM to wipe out programs before tests, so I just moved my programs to the disk. Then they started checking that so I wrote the programs during the test (it was still less work). The point is, students will always have ways to tweak their calculators. As others have mentioned, it's better to design tests where that doesn't matter. Nov 28 '17 at 14:55
• Sigh.... I will never understand why schools, teachers, SATs, etc. think there is any value to writing test questions which require a calculator. It's really not that hard to write problems with purely analytical solutions. Nov 28 '17 at 16:19

I received my bachelor's degree in mathematics in 1970. I didn't own a calculator.

There were some adjustments that helped with no-calculator tests:

• Many of my exams had ten points per question. 9 of the points were for clearly showing correct working. One point was for getting the right answer. A student who understood the material but was bad at arithmetic could get 90% without a single correct answer. A student who depended on a fancy calculator could miss more points for not showing all their work.
• The exam booklet included, at the back, any trig and similar tables we were going to need. Answers only had to be to the rather low precision supported by those tables.
• Questions were designed with easy numbers. For example, fractions would often simplify by just crossing out common factors.
• Questions were structured to minimize difficult arithmetic. For example, ask for the variance rather than the standard deviation, but also ask what they would have done differently to get the standard deviation.

Given the problem of the modified calculators, you can go in one of two directions. The first is real world. Full Internet access, statistical calculators etc. The other is to go back to the 1960's, and design tests for no calculators.

• Neat! Can I bring in a slide rule! Can you promise no polar-to-rectangular conversions requires? Nov 26 '17 at 2:22
• @PieterGeerkens If polar-to-rectangular conversion were required, the exam booklet would include low precision sine and cosine tables. Nov 26 '17 at 3:17
• +1 for the "real world"-approach. Seems like that's the best approach for providing students with a quality education.
– Nat
Nov 26 '17 at 6:23
• @PieterGeerkens, does your slide rule not have trig functions? Time to upgrade... Nov 27 '17 at 12:46
• There's a limit to how much no-calculator you can do with statistics. For example, there's so much arithmetic involved in even a small two-way ANOVA test that students would be hard-pressed to get even one problem done in a typical exam period, and tables big enough to interpolate a p-value from an F-test would take up a small book.
– Mark
Nov 27 '17 at 18:58

Don't use the calculators. The final number you get in a math/stat exam is not that important, is it? Have them write down the standard deviation formula, instead of having them calculate it by pressing two buttons. Find ways around not using the calculator. @Geoffrey suggestion is a good one. Are you interested in the correct number or in them understanding the meaning of variance and how it is calculated?

I am against using a calculator in any exam unless you get to very high levels of math or physics, at that point you can have all the hacked calculators you want but you will need to use your brain 100 times more than your intro stats class.

In addition, I might tell the students that the calculators have been banned because of the cheating, or tell them they should focus on the process.

• "I am against using a calculator in any exam unless you get to very high levels of math or physics" My experience, both as a student (all levels of math, high school through graduate level physics) and as a teacher (high school through graduate level math), from the early 1970s through the mid 2000s, has been that the higher you get, the less one needs to have a calculator readily available, and this is true even for numerical methods courses (which become essentially applied functional analysis at high levels). Calculator usage at high levels becomes irrelevant, which is perhaps your point. Nov 26 '17 at 11:18
• I like this - Do you tell the classes that calculators are banned this year for the actions of a few? On one hand it spreads news of the calculator cheat, on the other it makes the class angry at those who cheat and demonstrates there are consequences. Nov 26 '17 at 18:41
• @Criggie great idea, that has to be done as well. Nov 26 '17 at 20:00
• I like the idea of telling the students that the rules have changed because of the cheating scandal; that might be the biggest educational lesson here. An alternative to banning calculators altogether would be to provide a bare-minimum model instead. (I just searched on Google and found quite a few models sold for under $2 each). It's hard to say how much this might help the OP because the current model isn't identified. Still, it might well be that these ultra-cheap calculators would be harder to hack, and perhaps could even be changed often enough to stay one step ahead of the hackers. – J.R. Nov 27 '17 at 22:26 • Don't tell them calculators are banned because of the cheating. Tell them calculators are banned because they do not need them and should focus on the process, just as you've said. Dec 1 '17 at 12:04 I question the assumption that the department buying calculators is infeasible. • Calculators that can do basic arithmetic are dirt cheap, as little as$2, and probably less when buying in bulk.

• If you need a scientific calculator, they can be had for $5-$10, again, probably less in bulk.

On the other hand, reworking the material to not require calculators, as suggested by some, would be a huge expenditure of time and effort, probably far outweighing the cost of buying calculators when you consider the value of people's time. Also there is merit to your original premise of giving students an aid for arithmetic.

I already gave an answer attempting to stay within the parameters of the question, but it has some downsides, as commenters noted. Departmental calculators is a nice clean solution with no downside other than cost, so perhaps it is worth reconsidering.

If cost truly is prohibitive, could you require students to pay for a calculator that you hold for them? Many programs charge things like lab fees. Could you do something similar?

Edit: to prevent cheating by bringing in an identical calculator, you could come up with a scheme involving calculators that differ in appearance. Someone suggested assigning different colors of calculator by row (not known in advance), for example. Though I don't see that comment now, so I can't credit who had that idea. Or you could make the calculator too unwieldy to sneak in--for example, by mounting it to a large flat board in some way.

• I suspect its more of a we want to work as always before. If that is the case then this is the cheapest option indeed. Nov 26 '17 at 21:30
• This answer hints at, but doesn't quite suggest, a compromise that I have seen used in some universities: use of a dirt-cheap basic calculator so that students do not have to waste time number-crunching (no long multiplication, short division etc) combined with tables for statistical functions, or other relevant functions that a scientific calculator could provide (logs, exponentials, trigonometry, compound interest tables), but also to design exams so that more mathematically complex questions are purely symbolic, whereas "applied" questions requiring numerical answers are kept simpler Nov 26 '17 at 21:37
• Eg: in an introductory stats exam, asking students to find the p-value of a two-tailed z-test given some summary data may be a reasonable way to distinguish which students have met the course objectives. A high-end calculator might crank the answer out with minimal understanding required. Given statistical tables, pen and paper, it is hand-calculable - but much time would be expended on laborious arithmetic at which competence is not an assessment objective. With tables & non-scientific calculator (+-×÷√) the arithmetic is not a time-hog but students must work step-by-step & show working. Nov 26 '17 at 21:51
• This is the only feasible answer for a real-world solution. You can legally require students to leave everything at the door and use cheapo, course/lab fee calculators during exams, even if cheating were not a demonstrable issue. (But since it is, it helps justify the constraint and the cost to HR/directors/department chair/students/etc.) Nov 27 '17 at 2:07
• @Xerxes I see no reason to assume the current exams are useless. Having students complete math problems with calculator assistance is a perfectly good way of testing knowledge in many fields.
– user24098
Nov 27 '17 at 14:20

You don't have to check all calculators. Make sure to announce that you will be checking a random sample of calculators and that students caught with modified calculators will be expelled (if that's possible, e.g. for serious academical missbehaviour) or otherwise severely punished.

That way they will think twice before bringing a modified calculator because the risk is huge.

Talk to the legal department to see if you can require a sample of students to hand in their calculators at the end of the exam and have them tested then or exchange them with faculty calculators and have them tested during the exam.

• Comments are not for extended discussion; this conversation has been moved to chat. Nov 29 '17 at 16:13
• Check OP's point 1. How does anyone recognise a modified calculator? -1.
– Tim
Dec 3 '17 at 16:55
• @Tim check the OP's info again. They can open up the calculator to check; it just takes a while. I think this is in fact a great solution, as it requires very little that is new and would stop a lot of the casual cheaters. Dec 3 '17 at 20:18
• So, going into an exam, how much time will be allocated for calculator checks? Would 30 mins do, or maybe an hour, before the exam could commence? This could be part of the real world.
– Tim
Dec 3 '17 at 21:06
• @Tim none. Students come in, 10-20 are randomly selected and their caculators exchanged for faculty ones. They are checked for modifications during the exam and given back at the end. Dec 3 '17 at 22:02

Give them a computer, not a calculator.

Most universities have computer labs. Use them for your exam. With some help from the IT department, you can make sure that they cannot communicate on the network, and that they contain exactly the software that you allow them to run.

Besides the practical aspects, I think it is a good thing if calculators disappear from the world. They are basically crippled tablets/phones/computers with a poor user interface. If it weren't for exams, they would be a relic from the 90s, like floppy disks and programmable VHS recorders. Giving them a computer is testing them on the same skills that they will need in real life today, not on an artificial crippled setup.

• @DaveNewton All universities already have computer labs; there is no need to buy anything probably. As for the calculator UI, I strongly disagree. A modern programming language with a REPL (Python, Matlab, R, Julia...) is a "computer calculator" with an infinitely better UI: it lets you review, re-enter and modify a formula, for instance, or define functions/macros, or save a data set to do several computations on it (mean/variance/filtering etc.). The only reason people like calculator UIs is because they are used to them, but they are inferior under every practical criterion. Nov 26 '17 at 11:31
• @DaveNewton "There’s a reason phone calculator apps have a calculator UX" — nope, the reason is that typing letters on screen "keyboard" is slow, tedious and error prone, when these letters are too small. So there have to be just a few most used keys (digits and some) to make it possible to press them without missing. But compared to a real full sized keyboard, "calculator" UI is a joke. Nov 26 '17 at 11:50
• -1 since the suggestion makes no sense in practice. It is common for a university to have 500 or more students in the combined sections of each first year class. I doubt there are labs that big anywhere; certainly not in all universities I know. Besides, a cluttered environment is very helpful to cheating; even with "only the exam booklet on your desk" policies some students manage to cheat, a lab environment would help them greatly. Nov 26 '17 at 13:21
• @MartinArgerami We have conducted computer-assisted exams for a first-year course with 300 students (in the Italian system, they do not all take the exam at the same time; I think we had ca. 100 people divided over 3 computer labs at the same time at most). I agree that it is complicated to scale this solution to 500 students taking the exam at the same time, but if that is the main issue "makes no sense in practice" seems a huge overstatement. Nov 26 '17 at 15:39
• @Federico: I disagree, it's not an overstatement at all, it is fact. Our current enrollment in our two variants of Calculus I, with the final exam coming in two weeks, is 340 and 583 respectively. And my university is "mid size" by Canadian standards. I don't think any computer lab on our campus has more than 30 computers, so we would have to organize some 30 different sittings for the finals of those two classes, as opposed to two sittings in the gym as we do. It makes no sense in practice. In any case, I would be more concerned with the facilitated cheating than with the logistics. Nov 26 '17 at 16:13

Are you testing your students ability to do 1950s grunt work putting a large amount of numbers into a machine in the correct order in a time trial, or their understanding of math? You do not need to have your students do "lengthy arithmetic calculations". Your tests don't even need to use numbers at all. Or calculators for that matter.

if you're going with the first approach, however, modifying the calculator to best fit the requirements of the test should be encouraged rather than punished.

• I find this quite presumptious. Working out a real world problem with real numbers can be quite a good test of knowledge. And artificial limitations on what resources can be used in an exam setting are defensible in many cases.
– user24098
Nov 27 '17 at 16:06
• Arguably, student "understanding" may best be shown by answering applied questions like "Should we make this investment?" or "Can the bridge feasibly meet these restrictions?" or "Does the treatment show evidence of improvement at the 5% significance level?"; and all of those require a number to make said decision. Dec 11 '17 at 18:30

Just compose problems in the way that requires understanding rather than mechanical skills and make all calculators totally useless. For example, instead of asking "What is the antiderivative of $x^n$ with respect to $x$?" ask "What power function has an antiderivative equal to its square?". Now I challenge anyone to find a calculator that will help with this form of the question or a student with solid knowledge of algebra and calculus who will find the second question much harder than the first one.

• Obvious it depends on what you mean by "solid knowledge," but sadly I do teach students who apparently have no reading or reasoning ability and learn (any subject) only by rote, so that they could easily answer the first question without aids but would have trouble deciphering the meaning of the second. Nov 26 '17 at 1:35
• @AlexanderWoo Those are obsolete. Computers (or even some modern calculators) have superior performance and are easier to program. So who cares about them? If they don't experience cold anger, frustration, and the immense drive to get ahead when outperformed by a machine that is not their own creation, do they deserve to be classified as "homo sapiens" for the education purposes? Nov 26 '17 at 1:49
• We care about them because they are made in the image of God (substitute your preferred translation). Nov 26 '17 at 2:39
• We care about them because it is our job to care about them. Nov 26 '17 at 5:30
• +1, because the idea that students should be focused on demonstrating proficiency in human skills seems like the correct logic. Trying to remediate the practice of teaching humans to perform mechanized processes seems regressive.
– Nat
Nov 26 '17 at 6:13

Firstly let me welcome you to the 21st Century. :-)

"Calculators" went out with the dinosaur, people use smartphones now. So you're involved in the classic institutional mindset where you're trying to operate without reference to the real world and falling way behind it in the process.

The students do have calculators, smartphones and tablets.

Your tests should ideally not contain elements that test their ability to operate their electronic aids. But on the other hand they will have access to these aids in the real world - who actually doesn't use these things in the real world ?

So I'd suggest the correct policy is to :

• Structure exams to provide all the required information. Memorizing formulas is pointless so testing they can is pointless. All it does is bias tests in favor of people with good memories regardless of ability to apply their knowledge, so ...

• Test ability to apply knowledge, not ability to memorize things. We almost all nowadays carry about with us a tiny device capable of accessing almost any information we want. Could we please stop testing pupils on their ability to memorize stuff and rather on the ability to use what they can know.

• Exams may be the problem rather than the solution. We should really be moving away from exams (two hours of panic should really evaluate four or five years of work ??) and move to assessment based evaluation. The later gives a more consistent picture than some two hour exams that can be failed simply due to stress (which is huge). Shift your courses to assessment and away from the antiquated formal exam.

• Numeric calculations should deliver minimal points in an exam.

It doesn't matter one iota whether they can get the calculation right or wrong in a high-stress two hour exam. It proves almost nothing. Fine, it might be relevant if I was testing astronauts for the extremes of operating conditions they might have to deal with. Most people work at desks, don't have to do in-your-head calculations that decide life-or-death. People that do typically have to undergo specialist testing anyway. So ditch the numerics and stick to the theory and making them demonstrate they understand it.

• Statistics I can think of no less useful a thing than wasting test time on calculating statistics. This was only of practical use when people had to understand the operation of e.g. log tables (as we did when I started studying) because it was a relevant skill. But now ? It proves nothing but that they can type do numerical calculations under stress ( or can type accurately under stress ). It's devoid of practical value. Don't bother. Test the understanding of what they stats mean, not the ability to calculate them.

Stop having calculators all together. We would prefer not to resort to this as we don't think forcing students to do lengthy arithmetic calculations is the best way to test them. We could try to avoid such things however sometimes it is simply necessary to ask such questions, for example, in an introductory stats class we would like to ask students to find the standard deviation of a set of data points. Asking them to do this without a calculator seems unfair however we can't simply avoid asking such questions if we want to test the students properly.

As I've suggested, this is not testing them properly. It's testing the ability to type into a calculator (or do mental arithmetic) under stress - quite useless skills when they'll spend almost their entire lives walking around with pocket devices that do it all better and more accurately and they'll often get away with just cut and pasting data in.

Aim to test their understanding of what those statistical number mean and how useful they are in decision making. The mechanical act of do the calculation is simply the trivial application of formula in these cases - very, very few points or time should be allocated to this in an exam.

Taking action against the group responsible for making the calculators. ... As far as I can tell they are not committing any crimes.

Depends on local laws. I'd strongly suggest getting the state body that governs your exam and education system involved. You might, at a worst case, consider getting your institute to sue them for the costs of dealing with the cheating. Clearly they knew it was cheating as the mechanism to activate the functionality is not straightforward.

Simply ignore the problem. This is obviously not ideal as using these calculators gives students a clear advantage over those without them. Additionally, students using them often don't need to learn how to perform various calculations and can instead just plug in the various values and have the answer come out.

Simply admit it's not a problem.

Provide students with information they need to solve a problem or develop an answer. Focus on testing ability to apply information. Forget completely about memorization and calculation - these are certainly not useful tests. There are much better ways to test a person's memory (ask a psychologist) and much better ways to test their ability to calculate and type under stress. So test what they understand about the fundamentals of the subject, and their ability to extract meaning from results.

• "It's testing the ability to type into a calculator (or do mental arithmetic) under stress - quite useless skills" In my field, the ability to be able use the derived equation to arrive at the right quantity is quite as useful as, say, the ability to correctly react to street signs when driving (as opposed to answering questions about what you should do). Please take into account that in the (chemical, biological, ...) lab we often do not have the equivalent of backspace or undo. Yes, the exam may be a more stressful situation - but that is equally true for any other skill tested in the exam. Nov 28 '17 at 12:20
• @cbeleites I'm not quite clear what you're saying, but are you saying that testing candidates specifically for ability to thrive in stress is desirable ? My view is that there's enough stress without making it relate to things we no longer need to prioritize in normal working life. A stress-free exam is of course impossible (well mine never were :-) ). If a particular field needs to test for stress response then that can be done more effectively without conflating it with tests of core understanding, IMO. Nov 28 '17 at 12:29
• No, I'm not a fan of artificially increasing exam stress. But there are fields/subjects where those old-fashioned calculators are still in regular use and including them in an exam is IMHO sensible, e.g. rule-of-three calculations in chemical or biological labs. (Where incidentally you may be willing to expose a $3 calculator to the risk of drowning in acid or catching a microbiological contamination, but maybe not your smartphone. This may change when voice control becomes more widespread - but that again won't be suitable for exams...) Nov 28 '17 at 13:58 • I think this answer has some very good points, as somebody who worked on safety and time critical systems, there was "stress", but when it really, really mattered, the time limit was never the #1 priority, it wasn't even up in the top 10. What really mattered was reliability, which involves tasks like doing the math again, checking the schematics again, checking things from a different angle, testing the code under a different scenario, etc. Finishing a design sooner is important, but I found no real world task that was quite like doing exams in college. Class projects are very relevant though – jrh Dec 3 '17 at 18:17 • This answer shows an immense lack of understanding of current academic conditions, such that I presume the respondent is not actually a college teacher. The highlight is probably: "We should really be moving away from exams...". In practice, e.g., I have a friend who's taught CS at a global top 10 university in the U.S. for many years. He's dealing with such a rising/overwhelming amount of cheating on assignments (much like OP here) that he's been forced to cut all assessments and have only in-class tests. Comments that this is easy to fix arise only from abject ignorance. Dec 11 '17 at 18:40 We haven't experienced cheating as sophisticated as described in the question. But there have been issues, and we have been moving towards a no-calculator policy. Over the last few years I have taught all levels of calculus and linear algebra, all with a no-calculator policy. In linear algebra, in particular, row-reduction often requires doing arithmetic with fractions, and I remember years ago the students frantically punching their calculators (so much that I have indeed check that they were doing some related calculation); still, since the no-calculator policy, no issues have arisen. • IMHO, any matrix operation should only ever be done once in a test ever, after that all matrix calculations should be done by computer. In fact quite a few students have totally wrong view of matrix math because they computed things by hand. By calculating in computer you free them to thinking about symvolic manipulation and not number crunching Dec 3 '17 at 9:47 • A student who really understands row-reduction should be able to express the algorithm for it without actually having to perform that algorithm by hand. In practice, homework assignments where students have to code up the process would be great, or an exam done in a computer lab (depending on the institution's situation; some colleges have tons of computerized labs for this exact reason while others don't) would be a way to do it on an exam. – Nat Dec 9 '17 at 4:12 • @joojaa: as someone who multiplies matrices daily in several areas of my research in pure math and quantum information, I couldn't disagree more. Dec 9 '17 at 5:21 • @Nat: are you claiming that students can learn row reduction without doing many examples on their own? I would like to see that. Dec 9 '17 at 5:24 • @MartinArgerami I think a lot of students go to college already knowing row-reduction (even if they don't realize it). In grade school algebra, they have to solve linear equations to find values for$\left\{x,y,z\right\}$, which is often done via row-reduction that results in a diagonal matrix. Then at the college level, all ya really need to do is remind them of that fact, pointing out that the final product needn't be a perfect diagonal matrix anymore. (Also, I guess, you have to show them that what they were doing was getting a diagonal matrix. But they're already trained on it.) – Nat Dec 9 '17 at 5:30 One option I've sometimes seen used is to give students a small lookup sheet with the calculations they'll need for the exam. So if one of the questions in the exam is "find the mean of 3 and 8", the sheet would include the information that (3+8)/2 = 5.5 along with various red herrings. It will take some work to set up and it's not practical for all situations, but sometimes it's an option. Re. the idea of the department supplying calculators: you can deal with the problem of students sneaking in a second calculator and swapping it out during the exam by marking the department calculators in a visible way. "Today everybody in Row 1 gets the yellow calculators, Row 2 gets green, ..." etc. Then it's pretty obvious when somebody's not using the calculator you supplied. • I really dislike exams that actively try to mislead students. Its not a true test of their abilities, its insincere and just unfair. Nov 26 '17 at 10:18 • @Polygnome Do you consider multiple-choice exams to be insincere and unfair? That's all I'm talking about here - except that students are presented with multiple possible calculations, and have to choose the one that's relevant, rather than being given the answer options directly. Nov 26 '17 at 11:58 • I do consider multiple-choice exams bad, especially in STEM-Fields. At my university, they do not happen in STEM exams, I've only seen them being used in the soft sciences. And its always the same with them: Either they are blatantly obvious, or they use language that is purposefully deceiptive to create the illusion that you have to think about the question, while all they do is try to trick you into answering something wrong that you know better. If you want to know a formula, ask "How is the standard deviation calculated", not use MC with contrived examples and questionable notation. Nov 26 '17 at 13:45 Every calculator can be put "on steroids" I am a reverse-engineer nerd, fiddled consistently with calculators (albeit never used for cheating) and can tell you that since someone found out the potential of calculator-modifying there is nothing you can do to stop it unless you provide calculators. Even in this scenario a student could sneakily switch the one he has on the table.... Every calculator, even the simplest of the Casios can be reverse engineered to display messages from e.g. an Xbee on its screen. Trust me. It is not easy. Dont be too harsh on the original perpetrators... Punishment-wise Id make a distinction on who just bought the modified calculators and on who actually carried out the mod. "Just buy" are the ones that deserve the biggest punishment, so determined at cheating that spent money on buying cheating hardware. Actual minds behind the reverse-engineering and modding (provided that they are the original makers of the mod, not just script kiddies), should be punished, but keep in mind that as far as I know it takes the very brightest of the pack from your average engineering class to successfully reverse engineer and modify a calculator. Try to give this as a lab task and see... Honestly, regardless of the grades they are getting, they probably will prove to be the best engineers after school. Don`t kick them out please! Modify your tests It is entirely possible to design tests not to require a calculator (in my engineering college it was basically forbidden on every test), personally I believe such tests are the best one as they require more symbolical calculation. • I have to disagree with your middle statement. It doesn't matter if they are selling them or just using them, they are cheating. At my uni, that is an instant fail, they might expel them too, I'm not sure. It's no different to plagiarism for essays or sneakily reading a cellphone during a closed book exam. Dec 3 '17 at 5:50 • IMHO there is a difference between "cheating" and "cheating while showing you already have better revesre engineering skills than many alumni". No really try to put a calc on steroids and see how hard it is to end up with a neat job! Dec 22 '17 at 22:28 As Pat Shanahan suggests, just don't give credit where you can't see the work. Liberal use of the phrase "Show all work" should solve some of your issues. If somebody is using a contraband calculator to skip steps on a problem, they get very little credit for the solution. The issue you're not addressing, though, is cheating. Using an unauthorized calculator is cheating -- no ifs, ands, or buts. Protecting academic integrity should be an important part of what you strive to do, and if honest students feel disadvantaged because many students around them are cheating, that is a very poor outcome. I suggest a) reminding the students beforehand that unauthorized help of any form, including improper calculators, on an exam is an academic honesty issue, and will be treated as such, b) exams will be designed so as to minimize the amount of help that such a calculator can provide (and then try to do that!!), c) calculators might be spot checked during exams, and d) getting caught with such a device during exams will be treated as per university policies on violations of academic honesty. While less than ideal, I suggest that spot-checking calculators of students who lose credit on a previous exam for not showing work might be an effective strategy. I suggest that if one or two students get caught every now and again, the practice will eventually stop -- especially at US universities, where repeated violations will result in separation. • And then you get the guy who speeds up his calculus exams by memorizing integral tables. Dec 7 '17 at 16:43 My Cal II professor got it right - he had two versions of the test: # Calculator-free (default) This version had small numbers - typically 1-3, maybe 4 tops. The arithmetic was really simple, and he would give you points for showing your work (though you could get full marks if you got the answer correct without the work. But without the work and an incorrect answer then you'd get zero, so you may as well just show your work - you could get 70-90% of the points by showing correct work with wrong numbers). # Calculator-aided I never took one of these tests, so I don't even know what was on there, but he warned us that if you had a calculator it was because you needed it, or you wouldn't be able to actually finish the test. • What is the point of offering two versions? It seems like a superfluous conundrum to present the students with, and making grading equivalent seems quite hard. – user24098 Nov 28 '17 at 12:00 • I don't think he really offered the second version - I'm fairly sure it was just used as a threat. Nov 28 '17 at 15:55 Two suggestions: (1) Unless the calculators are very sophisticated, ensure that full marks will only be given if all steps of the calculations are shown (though I would need information about the type of questions asked). (2) Make sure that only one type of calculator is allowed in the exam and have the department provide that model for the exam and then require that the student return the calculator after the exam. • Your option (2) is consider and dismissed by the asker in the third paragraph of their question. If you still think it would be a viable option, your answer would be improved by explicitly addressing the concerns raised by the asker (i.e. mainly the cost of acquiring and maintaining the calculators, and the possibility of students still smuggling in their own modded calculator of seemingly identical type). Nov 26 '17 at 0:10 • I was left with the impression that the calculators were to be supplied to the students at the start of the academic year. – jim Nov 26 '17 at 0:13 • The question mentions statistics. For any stats question more advanced than a simple "find the mean" or "find the variance", showing all the steps is a lot of writing. Do you want your students to be writing out two or three pages of intermediate steps to get the answer? Worse, do you want to have to grade that? – Mark Nov 27 '17 at 19:10 • I was thinking of perhaps something along the lines of showing writing which was the appropriate formula to find (eg) the standard deviation then use the calculator as required, essentially following the advice of the suggestion given by Patricia Shanahan – jim Nov 28 '17 at 19:39 We have more computers than some, apparently. https://www.respondus.com/ Our university uses a product called LockDownBrowser. Once the student begins the test the application full-screens itself, and prevents them from navigating away from the test. A virtual calculator is could be displayed when necessary to do the math. I don't know the exact details, but many instructors use it. The students put all permitted materials on top of the desk, and the rest stays either below the desk or somewhere else out of reach. Some have the students leave there other materials in their lockers on test day. • Lockdownbrowser does not address actual issue in the age of smartphones, and behaves like malware from a systems point of view. Nov 27 '17 at 2:07 • Since you have no imagination: pepijndevos.nl/2016/07/10/… Nov 27 '17 at 2:37 • @Joshua There are maybe 2 students per semester taking math that could maybe do this. They obviously are doing the test in class and have no opportunity to use a VM. Their student don't have access to any software for that and the students are standard users and not permitted to install any software. Nov 27 '17 at 2:50 • I was asked to take a look at LockDownBrowser once. Took me only a few minutes to break out of it. – Mark Nov 27 '17 at 19:12 • It doesn't take students with programming savvy to break out of things like this; it takes entrepreneurs with programming savvy to produce and sell a user-friendly hack to students...entrepreneurs like those who hacked and sold calculators to the OP's students. Possibly if the computers that are being used are always outside the access of students (and the entrepreneurs) this program would work, but installing it on students' personal laptops is never going to be foolproof. Nov 27 '17 at 22:39 If you don't want to change you tests or testing habits, here's a less impractical way of checking calculators, especially if you combine it with DonQuiKong's suggestion of taking a random subset: check calculators after the exam. Just make a couple of students write their name on their calculators and hand them in with the exams. That way you have as much time as you want to test them, find the password to activate it, or even just unscrew the back to look if the electronics are standard. That, with fair warning of an exemplary punishment such as automatically failing the class (or being expelled as suggested elsewhere), should be a good dissuasive measure. If this is during a testing period and students need calculators immediately afterwards, arrange to lend them school-issued calculators as a temporary replacement, otherwise just arrange with them to pick the calculators up the next day or something like that. For other considerations such as swapping modded for normal calculators, I remember when I used to take tests we had to leave our bags with phones and all at the entrance of the class on test days. Make them bring to their tables only what's strictly necessary: pen, paper, calculator, snack, etc. but nothing in which they could hide a second calculator. • RE: Just make a couple of students write their name on their calculators and hand them in with the exams. That way you have as much time as you want to test them. I don't think this would work. How many students are using their calculators in classes other than the class in question? Considering that many exams for different courses are scheduled within the same rough timeframe, it's entirely possible that a student would have a need for the calculator again in a matter of mere hours. – J.R. Nov 27 '17 at 22:03 • @J.R. hence the 4th paragraph in my answer. Nov 27 '17 at 22:05 • If you're going to loan them school-issued calculators as a temporary replacement, you may as well just have them use those calculators during their exam. It's less of a headache. – J.R. Nov 27 '17 at 22:09 • @J.R. Except now you don't need enough calculators for the full class, just the amount that you want to check - so that mostly solves the budget problem of school-issued calculators. Nov 27 '17 at 22:38 • If budgetary restrictions permit you to only buy N calculators, then give N students those calculators before the exam starts. When they are finished with their exam, give them their personally-owned calculators back. This would be as effective as your suggestion except that it doesn't give you a week or so to check for modifications – but I'm not sure the dept wants to get into that business anyway. – J.R. Nov 27 '17 at 22:42 A calculator provides approximate numeric solution only and would not be able to provide answers that cannot be represented with the help of its finite decimal display. Think tasks with the answers like sin(1/5), sqrt(3), 2777/4879 or similar. They can only be obtained analytically. This would reduce the problem to the few very high end models and also laptops are capable of running (rather expensive) symbolic math engines like Maple V. Also, such tasks would show students why ability to solve without calculator is still valuable. • There are free symbolic packages out there, and if the people are swapping the electronics inside the calculator then they can as well put in a SOC thats perfectly capable of running a proper computer environment. Do not underestimate modern electronics for 5-20 dollars you get a full computer. Hell, squeeze a raspberry zero on your calculator and you get mathematica for free. Dec 2 '17 at 21:25 Some of these points have been brought up in other answers/comments, but there's still value in collecting them in one answer: 1. Evaluate your students in regular classes. Ask them questions, see how they respond. You should already have some idea of how well students are learning before the test. If students do well on tests but not when you actually talk to them, this is a red flag (Not necessarily a red flag for cheating. Even if they aren't cheating, there's likely something that you should be addressing.) 2. Have calculator-free tests At least some of your tests should be calculator-free. You should be testing your students' understanding of the material, not their ability to perform calculations. Ask yourself what you expect your students to learn, and how that can be tested. 3. Ask for calculator instructions If you really want to test students' ability to use a calculator, you can just ask them “What buttons would you press to get the answer to this question?” and not actually give them a calculator. This should be used sparingly, but is another tool available. 4. Redistribute Take all the students' calculators and randomly distribute them between the students. 5. Offer a bounty Combined with above: offer a bounty to students who find that the calculator they were given was modified. 6. Random sample You don't need to check every calculator, just a random sample. If the penalty is harsh enough (at the very least, they should be given a 0 for the course, if not expelled), this will still be a strong deterrent. 7. Look at legal options. Your causes of actions against the people making the modifications aren't too strong. Maybe tortious interference. However, if you can get the maker of the calculator involved, they have much stronger causes of action. For instance, if someone is selling a modified calculators and presenting them as normal, that's a violation of trademark. 8. Pay attention to use Walk around the room and watch how people are using their calculators. Are they being furtive? Using their calculators on questions that don't require any calculations? Pressing keys that don't make sense for the problem? 9. Look at patterns A modified calculator is going to be more useful on some questions than others. Look at whether there are students doing better on those types of questions. You can even deliberately make questions that only students with modified calculators can answer. Also, it seems like this issue could be reduced if classrooms had cameras recording students taking tests, but that's probably not feasible in the current culture. The only feasible way to have secure calculator use is to provide them. I guarantee you that students this resourceful and determined will outsmart any other method. If calculator use is then desired, the only question that remains is how to make it affordable. Treat them like required customized textbooks only available at your store. Require each student to buy a school owned calculator equal to the cost of a calculator. The school maintains custody of this exam calculator. Use this to fund purchases. Provide a calculator at the time of the exam and collect afterwards. At the end of the year, students may take possession of the calculator or sell them back to the school at a discounted rate, just like textbooks. If you make the discounted rate enough, students will keep them and sell them elsewhere if you so desire. The important part is that no student ever has custody of a calculator used for an exam. The school always does. There are a few more options not listed in other answers. They are a lot more devious but may be less successful. • Start modding and selling calculators yourselves. Obviously don't let the students know it is you. Program the forbidden functions to produce incorrect results when specific inputs are present. Then use those inputs only on tests. Don't use them for homework problems and such so the answers in those cases are correct. There might even be money to be made. • Examine some of the modded calculators. See if they were programmed well. If there are glitches with some inputs then craft the tests to trigger those glitches. • Calculations done in software have limitations. There are problems with rounding and loss of precision for example. Design exam questions that will put any calculator into problem areas but wouldn't cause problems for a student not using a calculator. • Start modding and selling calculators yourselves openly. Require that only your modded calculator can be used for some questions. Have the calculator produce encoded results or systematically altered results. Other calculators, modded or not, would not be able to produce those results. One example might be to produce the result and a check value. • In a word... "ethics" Nov 26 '17 at 8:50 • Thanks @Criggie for confirming that all parts of my answer are good ethically. Nov 26 '17 at 9:23 • Have the calculator produce ... altered results. Run into at least ethical problems when students use the same calculator later in their career. Nov 26 '17 at 15:28 • @Criggie and point 3 is good, if you can write an exam question that fits At your service, Sir. Find the tangent of$10^{15}\pi\$. Asymptote outputs -0.24308... and I doubt that calculators will perform any better :-) Nov 27 '17 at 0:03
• This slightly mad answer might be termed the Lex Luthor solution. Don't try this one at home, folks. No offense, poster. Note: I haven't actually downvoted, since I've always had a sneaking admiration for supervillainy. Nov 30 '17 at 11:49

I think you should just ignore it. If you try checking for them, or stopping them, there will always be a workaround eventually. If all they're getting is the right answer then that's not a problem. You should look at the way the tests are graded, because on all of the tests that I've taken, if you don't show work then the problem is wrong regardless of the answer, and this is the way it should be to make sure students actually know what they are doing, not just typing in numbers.

• Banks get robbed, no matter how hard they and the police try to avoid it. We should stop trying, then? Or maybe cheating on exams is no big deal, "everybody cheats, anyway"? Nov 26 '17 at 15:51
• @RolazaroAzeveires: This is different from robbing a bank. The students are paying their own money to learn this material. If they cheat, that generally indicates not actually learning it. So they are wasting their time and money. But that's their problem. Nov 27 '17 at 22:24
• They are robbing the other students, by ending up with a diploma showing the same qualifications, possibly even with better grades. It can make a lifetime of a difference. And the other students are paying also. Nov 28 '17 at 3:02